A CAFC is to be made of 20% silicon carbide (SiC) fibersembedded in a matrix of

Question

A CAFC is to be made of 20% silicon carbide (SiC) fibersembedded in a matrix of 80% polycarbonate, with an original lengthof 36%cm. When placed in tension with a load of 240,000 N underisostrain conditions, the deformation must be 1.0mm. Assumingelastic conditions, determine:

A) The necessary cross sectional areas in cm3 . ofSiC and polycarbonate.

B) The fraction of the load force supported by the fibers.

                                                            Elastic Modulus(Gpa)              Tensile Strength (Mpa)

SiliconCarbide                                           400.0                                                     3900

Polycarbonate                                                2.4                                                         65

Explanation / Answer

deformation for SiC = deformation for polycarbonate (FL/AE)SiC = (FL/AE)polycarbonate Fs*L/(0.2A*400) =(240000-Fs)*L/(0.8A*2.4) Fs/(80) = (240000-Fs)/(1.928) 0.0125Fs = 124481.33 - 0.51867Fs Fs = 234353.1 N (a) Fs*L/(0.2A*400) =0.001 234353.1*0.36/(0.2A*400*109) = 0.001 A = 1.0546*10-3 m2 cross sectional area of SiC = 0.2*1.0546*10-3m2 cross sectional area of SiC = 2.1092*10-4m2 cross sectional area of polycarbonate= 0.8*1.0546*10-3m2 cross sectional area of polycarbonate= 0.84368m2 (b) fraction of the load force supported by the fibers = Fs/ F fraction of the load force supported by the fibers =234353.1/240,000 fraction of the load force supported bythe fibers = 0.9765

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